Second‐order sliding mode output feedback controller with adaptation

Summary An adaptive second‐order sliding mode output feedback controller is developed to deal with the case that the bound of the uncertainty/perturbation is unknown. The control structure consists in a twisting controller and a super‐twisting observer to estimate the unmeasured variable. The gains of the controller and observer are parametrized in terms of a scalar gain, such that increasing these two gains, it is always possible to find values to (finite‐time) stabilize the closed loop system. Finally, adaptive gain laws are provided to increase the controller and the observer gains until the closed loop has been stabilized. The main technical contribution of the paper is to give a sound and non‐trivial Lyapunov analysis of this otherwise intuitively simple idea. We illustrate the performance of the proposed controller by means of experimental results in a laboratory setup.